THE QUARTERLY JOURNAL OF PURE

AND APPLIED MATHEMATICS.

CAMBRIDGE:

PRINTED BY W, METCALFE & SONS, TRINITY STREET, CORNER OF GREEN STREET.

THE

QUARTERLY JOURNAL

OF

PURE AND APPLIED

MATHEMATICS.

EDITED BY

J. J. SYLVESTER, M.A., F.R.S.,

PROFESSOR OF MATHEMATICS IN THE ROYAL MILITARY ACADEMY,
WOOLWICH; AND

N. M. FERRERS, M.A.,

FELLOW AND TUTOR OF GONVILLE AND CAIUS COLLEGE, CAMBRIDGE:

LUCASIAN PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF CAMBRIDGE;

A. CAYLEY, M.A., F.R.S.,

SADLERIAN PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF

CAMBRIDGE; AND

M. HERMITE,

CORRESPONDING EDITOR IN PARIS.

VOL. XI.

ὅ τι οὐσία πρὸς γένεσιν, ἐπιστημὴ πρὸς πίστιν καὶ διάνοια πρὸς εἰκασίαι· ἔστι,

LONDON:

LONGMANS AND CO.,

PATERNOSTER ROW.

CONTENTS OF VOLUME XI.

On the Relation between the Angular Velocity about and the

Angular Velocity of the Instantaneous Axis of a Body revolving

spontaneously about a fixed point, and on the Axes of Greatest

and Least Mobility. By William Walton

On the Quartic Surfaces (*XU, V, W)2 = 0—continued from Vol. x.,

p. 34. By Prof. Cayley

General Solution and Extension of the Problem of the 15 School

Girls. By Andrew Frost

Mathematical Notes. By W. H. Besant

PAGE

15

26

38

42

Note on a Binary Evectant Form. By Samuel Roberts

Electro-Dynamics. Ampere's Theory of the Solenoid. By Percival

Frost

47

57

On the Algebra of Magic Squares. No. I. By Joseph Horner

Note to the Article on Porisms, Quarterly Journal, No. 30. By

Joseph Wolstenholme

66

On the Stress exerted by a Rigid Body on a Fixed Point rigidly

connected with the Body, which is revolving spontaneously

about the Point. By William Walton

69

Note on Euclid, Book VI. Prop. 7. By J. F. Wolff, Jun.

Theorem on the Action of an Electric Current in a Helix wound

on a Cylinder of any Form upon the Pole of a Magnet. By

Percival Frost

77